%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL009-1 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n029.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 04:44:46 EDT 2024 % Result : Unsatisfiable 58.71s 58.77s % Output : CNFRefutation 58.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL009-1 : TPTP v8.2.0. Released v1.0.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Jun 18 16:27:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.51/0.56 start to proof:theBenchmark % 58.69/58.75 %------------------------------------------- % 58.69/58.75 % File :CSE---1.7 % 58.69/58.75 % Problem :theBenchmark % 58.69/58.75 % Transform :cnf % 58.69/58.75 % Format :tptp:raw % 58.69/58.75 % Command :java -jar mcs_scs.jar %d %s % 58.69/58.75 % 58.69/58.75 % Result :Theorem 58.150000s % 58.69/58.75 % Output :CNFRefutation 58.150000s % 58.69/58.75 %------------------------------------------- % 58.71/58.77 %-------------------------------------------------------------------------- % 58.71/58.77 % File : COL009-1 : TPTP v8.2.0. Released v1.0.0. % 58.71/58.77 % Domain : Combinatory Logic % 58.71/58.77 % Problem : Weak fixed point for B and L2 % 58.71/58.77 % Version : [WM88] (equality) axioms. % 58.71/58.77 % English : The weak fixed point property holds for the set P consisting % 58.71/58.77 % of the combinators B and L2, where ((Bx)y)z = x(yz), (L2x)y % 58.71/58.77 % = y(xx). % 58.71/58.77 % 58.71/58.77 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 58.71/58.77 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem % 58.71/58.77 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 58.71/58.77 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb % 58.71/58.77 % Source : [MW88] % 58.71/58.77 % Names : - [MW88] % 58.71/58.77 % 58.71/58.77 % Status : Unsatisfiable % 58.71/58.77 % Rating : 0.27 v8.2.0, 0.29 v8.1.0, 0.30 v7.5.0, 0.29 v7.4.0, 0.35 v7.3.0, 0.32 v7.1.0, 0.22 v7.0.0, 0.21 v6.4.0, 0.26 v6.3.0, 0.24 v6.2.0, 0.21 v6.1.0, 0.12 v6.0.0, 0.33 v5.5.0, 0.21 v5.4.0, 0.27 v5.3.0, 0.17 v5.2.0, 0.14 v5.1.0, 0.20 v5.0.0, 0.21 v4.1.0, 0.18 v4.0.1, 0.21 v4.0.0, 0.23 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.14 v2.1.0, 0.38 v2.0.0 % 58.71/58.77 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR) % 58.71/58.77 % Number of literals : 3 ( 3 equ; 1 neg) % 58.71/58.77 % Maximal clause size : 1 ( 1 avg) % 58.71/58.77 % Maximal term depth : 4 ( 2 avg) % 58.71/58.77 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 58.71/58.77 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty) % 58.71/58.77 % Number of variables : 6 ( 0 sgn) % 58.71/58.77 % SPC : CNF_UNS_RFO_PEQ_UEQ % 58.71/58.77 % 58.71/58.77 % Comments : % 58.71/58.77 %-------------------------------------------------------------------------- % 58.71/58.77 cnf(b_definition,axiom, % 58.71/58.77 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 58.71/58.77 % 58.71/58.77 cnf(l2_definition,axiom, % 58.71/58.77 apply(apply(l2,X),Y) = apply(Y,apply(X,X)) ). % 58.71/58.77 % 58.71/58.77 cnf(prove_fixed_point,negated_conjecture, % 58.71/58.77 Y != apply(combinator,Y) ). % 58.71/58.77 % 58.71/58.77 %-------------------------------------------------------------------------- % 58.71/58.77 %------------------------------------------- % 58.71/58.77 % Proof found % 58.71/58.77 % SZS status Theorem for theBenchmark % 58.71/58.77 % SZS output start Proof % 58.71/58.78 %ClaNum:8(EqnAxiom:5) % 58.71/58.78 %VarNum:13(SingletonVarNum:6) % 58.71/58.78 %MaxLitNum:1 % 58.71/58.78 %MaxfuncDepth:3 % 58.71/58.78 %SharedTerms:3 % 58.71/58.78 %goalClause: 8 % 58.71/58.78 %singleGoalClaCount:1 % 58.71/58.78 [8]~E(f2(a4,x81),x81) % 58.71/58.78 [6]E(f2(f2(a1,x61),x62),f2(x62,f2(x61,x61))) % 58.71/58.78 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(x71,f2(x72,x73))) % 58.71/58.78 %EqnAxiom % 58.71/58.78 [1]E(x11,x11) % 58.71/58.78 [2]E(x22,x21)+~E(x21,x22) % 58.71/58.78 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.71/58.78 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 58.71/58.78 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 58.71/58.78 % 58.71/58.78 %------------------------------------------- % 58.71/58.79 cnf(9,plain, % 58.71/58.79 (E(f2(x91,f2(x92,x92)),f2(f2(a1,x92),x91))), % 58.71/58.79 inference(scs_inference,[],[6,2])). % 58.71/58.79 cnf(12,plain, % 58.71/58.79 (E(f2(x121,f2(x122,x123)),f2(f2(f2(a3,x121),x122),x123))), % 58.71/58.79 inference(scs_inference,[],[7,2])). % 58.71/58.79 cnf(13,plain, % 58.71/58.79 (~E(f2(a4,f2(f2(a1,x131),x132)),f2(x132,f2(x131,x131)))), % 58.71/58.79 inference(scs_inference,[],[8,9,7,2,3])). % 58.71/58.79 cnf(144,plain, % 58.71/58.79 (E(f2(x1441,f2(x1442,x1443)),f2(f2(f2(a3,x1441),x1442),x1443))), % 58.71/58.79 inference(rename_variables,[],[12])). % 58.71/58.80 cnf(146,plain, % 58.71/58.80 ($false), % 58.71/58.80 inference(scs_inference,[],[13,12,144,3,2,4]), % 58.71/58.80 ['proof']). % 58.71/58.80 % SZS output end Proof % 58.71/58.80 % Total time :58.150000s %------------------------------------------------------------------------------